We investigate the effects of the nearby interstellar medium (ISM) on the locally measured cosmic-ray (CR) spectra. Using the GALPROP code we explore how variations in the local gas and source distributions affect spectral features at low energies. Comparing with recent Voyager 1 measurements taken in the local ISM, we show that for a realistic interstellar gas distribution the data favour models in which there are no significant CR sources with ~150-200 pc of the Solar system, implying that the nearest dominant contributors to the low-energy CR flux are located at distances beyond this range. We find that the modelling supports the conclusions of Cummings et al. (2025) that there is a significant fraction of primary Boron in its observed spectrum at low energies. Our study shows that detailed modelling of the immediate Galactic environment is required to robustly infer Galactic CR propagation parameters from local measurements, and that accounting for nearby ISM structure can alleviate tensions between direct CR data and global propagation models.
Data from the Voyager probes have provided us with the first measurement of cosmic ray intensities at MeV energies, an energy range which had previously not been explored. Simple extrapolations of models that fit data at GeV energies, e.g. from AMS-02, however, fail to reproduce the Voyager data in that the predicted intensities are too high. Oftentimes, this discrepancy is addressed by adding a break to the source spectrum or the diffusion coefficient in an ad hoc fashion, with a convincing physical explanation yet to be provided. Here, we argue that the discrete nature of cosmic ray sources,…
The acceleration of cosmic ray particles and their propagation in the Milky Way and the heliosphere tangle with each other, leading to complexity and degeneracy of the modeling of Galactic cosmic rays (GCRs). The recent measurements of the GCR spectra by Voyager-1 from outside of the heliosphere gave a first direct observation of GCRs in the local interstellar (LIS) environment. Together with the high-precision data near the Earth taken by ACE and AMS-02, we derive the LIS spectra of Helium, Lithium, Beryllium, Boron, Carbon, and Oxygen nuclei from a few MeV/n to TeV/n, using a non-parameteriz…
Time-dependent cosmic ray modulation in the outer heliosphere: Signatures of a heliospheric asymmetry and model predictions along Voyager 1 and 2 trajectories
A Fit to the Galactic Cosmic Ray Hydrogen and Helium Spectra at Voyager 1 at Low Energies and Earth Based Measurements at Much Higher Energies with Identical Rigidity Independent Source Spectra for the Hydrogen and Helium Nuclei
Calculations of the Propagated LIS Electron Spectrum Which Describe the Cosmic Ray Electron Spectrum below ~100 MeV Measured Beyond 122 AU at Voyager 1 and its Relationship to the PAMELA Electron Spectrum above 200 MeV
新的旅行者测量宇宙射线电子之间的6-60兆电子伏超过122 AU是非常敏感的指标宇宙射线传播和加速在星系中在一个非常低的调制水平。使用蒙特卡罗扩散模型与源光谱与一个单一的光谱指数为-2.2在所有的能量，我们能够适应这个观察到的旅行者光谱和当代PAMELA电子光谱的能量范围从6 MeV到~200 GeV。这个频谱中有一个中断，但这个中断是由于传播效应，而不是主频谱的变化。这种突变是逐渐发生的，从能量大于2 GeV的能量开始，此时的能谱为~E^-3.2，然后继续下降到能量小于或等于100 MeV的能量，此时的能谱为~E^-1.5。在较高的能量下，由于同步辐射和逆康普顿效应产生的损失项约为E^2.0，使源谱的指数变陡1.0。在较低的能量下，这些项变得不重要，损失由扩散和逃离星系决定。在~0.32 GV以下，扩散项与β ^-1成正比（这也符合在旅行者号上测得的氢和氦的光谱），在1 GV时的值为3 × 1028 cm ^2 x s^-1，边界在+/-1 Kpc，这将符合旅行者号或其他类似的低能光谱。
We study the propagation and injection models of cosmic rays using the latest measurements of the Boron-to-Carbon ratio and fluxes of protons, Helium, Carbon, and Oxygen nuclei by the Alpha Magnetic Spectrometer and the Advanced Composition Explorer at top of the Earth, and the Voyager spacecraft outside the heliosphere. The ACE data during the same time interval of the AMS-02 data are extracted to minimize the complexity of the solar modulation effect. We find that the cosmic ray nucleus data favor a modified version of the diffusion-reacceleration scenario of the propagation. The diffusion c…
We have used new measurements of the B/C ratio in galactic cosmic rays at both low and high energies by the Voyager and AMS-2 spacecraft, respectively, along with propagation calculations using a truncated LBM to examine the implications of these new measurements over an extended energy range from a few MeV/nuc to 1 TeV/nuc. We find that the predictions from both the truncated LBM and the Diffusive Reacceleration model for GALPROP both agree with the Voyager and AMS-2 measurements of the B/C ratio to within +/- 10 percent throughout the entire energy range from 50 MeV/nuc to 1 TeV/nuc. The two…
The AMS experiment has recently measured the proton and helium spectra in cosmic rays (CRs) in the GeV-TeV energy region. The two spectra are found to progressively harden at rigidity $R = pc/Z >\,$200 GV, while the p/He ratio is found to fall off steadily as $p/He\sim\,R^{-0.08}$. The p/He decrease is often interpreted in terms of particle-dependent acceleration, which is in contrast with the universal nature of DSA mechanisms. A different explanation is that the p-He anomaly reflects a flux transition between two components: a sub-TeV flux component (L) provided by hydrogen-rich supernova re…
Using Leaky Box Model propagation calculations for H nuclei and a Monte Carlo diffusion propagation model for electrons, starting from specific source spectra, we have matched the observed LIS spectra of these cosmic rays measured by Voyager at lower energies and AMS-2 at higher energies, a range from ~10 MeV to ~1 TeV. The source spectra required are very similar rigidity spectra. Below ~6-10 GV the source spectra for both particles are ~P-2.25 and above 10 GV the spectra are ~P-2.36-2.40. This break in the source spectral index is not seen for He and C nuclei in a match of Voyager and AMS-2 …
A Comparison of the Galactic Cosmic Ray H, He and C/O Nuclei Spectra Measured Between ~5 and 500 MeV/nuc Beyond 122 AU at Voyager 1 with the Predictions of a Diffusion Model for Propagation in the Galaxy
A Study of the B/C Ratio Between 10 MeV/nuc and 1 TeV/nuc in Cosmic Rays Using New Voyager and AMS-2 Data and a Comparison with the Predictions of Leaky Box Propagation Models
Observations of the Abundances of Secondary Galactic Cosmic Rays from Z equals 5 to 28 Between 10 and 200 MeV/nuc Beyond the Heliopause by Voyager, Some Unexpected Anomalies and Their Interpretation Using a LBM for Galactic Propagation
Current-day cosmic ray (CR) propagation studies use static Milky-Way models and fit parametrized source distributions to data. Instead, we use three-dimensional magneto-hydrodynamical (MHD) simulations of isolated galaxies with the moving-mesh code AREPO that self-consistently accounts for hydrodynamic effects of CR protons. In post-processing, we calculate their steady-state spectra, taking into account all relevant loss processes. We show that this steady-state assumption is well justified in the disc and generally for regions that emit non-thermal radio and gamma rays. Additionally, we mode…
HelMod is a Monte Carlo code developed to describe the transport of Galactic Cosmic Rays (GCRs) through the heliosphere from the interstellar space to the Earth. In the current HelMod version 4 the modulation process, based on Parker's equation, is applied to the propagation of GCRs in the inner and outer heliosphere, i.e., including the heliosheath. HelMod was proved to reproduce protons, nuclei and electrons cosmic rays spectra observed during solar cycles 23-24 by several detectors, for instance, PAMELA, BESS and AMS-02. In particular, the unprecedented accuracy of AMS-02 observations allow…
Low energy cosmic rays are the major ionization agents of molecular clouds. However, it has been shown that, if the cosmic ray spectrum measured by Voyager 1 is representative of the whole Galaxy, the predicted ionization rate in diffuse clouds fails to reproduce data by 1-2 orders of magnitude, implying that an additional source of ionization must exist. One of the solutions proposed to explain this discrepancy is based on the existence of an unknown low energy (in the range 1 keV-1 MeV, not probed by Voyager) cosmic ray component, called carrot when first hypothesized by Reeves and collabora…
Power requirements for cosmic ray propagation models involving diffusive reacceleration; estimates and implications for the damping of interstellar turbulence
The local interstellar spectra (LIS's) for galactic cosmic rays (CR's) cannot be directly observed at the Earth below certain energies, because of solar modulation in the heliosphere. With Voyager 1 crossing the heliopause in 2012, in situ experimental LIS data below 100 MeV/nuc can now constrain computed galactic CR spectra. Using galactic propagation models, galactic electron, proton and light nuclei spectra can be computed, now more reliably as very LIS's. Using the Voyager 1 observations made beyond the heliopause, and the observations made by the PAMELA experiment in Earth orbit for the 2…
In this review, we first reassess the supernova remnant paradigm for the origin of galactic cosmic rays in the light of recent cosmic-ray data acquired by the Voyager 1 spacecraft. We then describe the theory of light element nucleosynthesis by nuclear interaction of cosmic rays with the interstellar medium and outline the problem of explaining the measured Be abundances in old halo stars of low metallicity with the standard model for the galactic cosmic ray origin. We then discuss the various cosmic ray models proposed in the literature to account for the measured evolution of the light eleme…
The $γ$-ray observation of interstellar gas provides a unique way to probe the cosmic rays (CRs) outside the solar system. In this work, we use an updated version of Fermi-LAT data and recent multi-wavelength tracers of interstellar gas to re-analyze a mid-latitude region in the third Galactic quadrant and estimate the local CR proton spectrum. Two $γ$-ray production cross section models for $pp$ interaction, the commonly used one from Kamae et al. (2006) and the up-to-date one from Kafexhiu et al. (2014), are adopted separately in the analysis. Both of them can well fit the emissivity and the…
We present a comprehensive discussion about the origin of the features in the leptonic component of the cosmic-ray spectrum. Working in the framework of a up-to-date CR transport scenario tuned on the most recent AMS-02 and Voyager data, we show that the prominent features recently found in the positron and in the all-electron spectra by several experiments are explained in a scenario in which pulsar wind nebulae (PWNe) are the dominant sources of the positron flux, and nearby supernova remnants shape the high-energy peak of the electron spectrum. In particular we argue that the drop-off in po…
Understanding the cosmic ray (CR) ionization rate is crucial in order to simulate the dynamics of, and interpret the chemical species observed in molecular clouds. Calculating the CR ionization rate requires both accurate knowledge of the spectrum of MeV to GeV protons at the edge of the cloud as well as a model for the propagation of CRs into molecular clouds. Some models for the propagation of CRs in molecular clouds assume the CRs to stream freely along magnetic field lines, while in others they propagate diffusively due to resonant scattering off of magnetic disturbances excited by MHD tur…
The recent measurement of the spectra of intermediate mass nuclei and iron nuclei carried out with the AMS-02 experiment provided us with the most complete set of data on cosmic ray fluxes to date, and allowed us to test the standard model for the transport of these particles through the Galaxy to the finest details. We show that the parameters derived from lighter primary and secondary elements in the cosmic radiation also lead to a good description of the data on heavier nuclei, with no need to invoke different injection spectra for such nuclei, provided the whole chain of fragmentation is p…
We recently proposed a method to constrain $s$-wave annihilating MeV dark matter from a combination of the Voyager 1 and the AMS-02 data on cosmic-ray electrons and positrons. Voyager 1 actually provides an unprecedented probe of dark matter annihilation to cosmic rays down to $\sim 10$ MeV in an energy range where the signal is mostly immune to uncertainties in cosmic-ray propagation. In this article, we derive for the first time new constraints on $p$-wave annihilation down to the MeV mass range using cosmic-ray data. To proceed, we derive a self-consistent velocity distribution for the dark…
The secondary-to-primary ratios are unique tools to investigate cosmic ray propagation mechanisms. In this work, we use the latest data of deuteron-to-helium~4 ratio and helium~3-to-helium~4 ratio measured by PAMELA combined with other Z$\leq$2 primary fluxes measured by PAMELA and Voyager-1, to constrain the cosmic ray acceleration and propagation models. The analysis is performed by interfacing statistical tools with the GALPROP propagation package. To better fit both the modulated and unmodulated low energy cosmic ray data, we find that a time-, charge- and rigidity-dependent solar modulati…
Cosmic rays are usually assumed to be the main ionization agent for the interior of molecular clouds where UV and X-ray photons cannot penetrate. Here we test this hypothesis by limiting ourselves to the case of diffuse clouds and assuming that the average cosmic ray spectrum inside the Galaxy is equal to the one at the position of the Sun as measured by Voyager 1 and AMS-02. To calculate the cosmic ray spectrum inside the clouds, we solve the one-dimensional transport equation taking into account advection, diffusion and energy losses. While outside the cloud particles diffuse, in its interio…
Low energy cosmic rays are modulated by the solar activity when they propagation in the heliosphere, leading to ambiguities in understanding their acceleration at sources and propagation in the Milky Way. By means of the precise measurements of the $e^-$, $e^+$, $e^-+e^+$, and $e^+/(e^-+e^+)$ spectra by AMS-02 near the Earth, as well as the very low energy measurements of the $e^-+e^+$ fluxes by Voyager-1 far away from the Sun, we derive the local interstellar spectra (LIS) of $e^-$ and $e^+$ components individually. Our method is based on a non-parametric description of the LIS of $e^-$ and $…
Cosmic rays (CRs) propagate in the Milky Way and interact with the interstellar medium and magnetic fields. These interactions produce emissions that span the electromagnetic spectrum, and are an invaluable tool for understanding the intensities and spectra of CRs in distant regions, far beyond those probed by direct CR measurements. We present updates on the study of CR properties by combining multi-frequency observations of the interstellar emission and latest CR direct measurements with propagation models.
In this work we aim at reproducing, simultaneously, the spectral feature at $\sim 10 \, \mathrm{TeV}$ in the cosmic-ray proton spectrum, recently reported by the DAMPE Collaboration, together with the spectral break at $\sim 1 \, \mathrm{TeV}$ measured by H.E.S.S. in the lepton spectrum. Those features are interpreted as signatures of one nearby hidden cosmic-ray accelerator. We show that this interpretation is consistent with the dipole-anisotropy data as long as the rigidity scaling of the diffusion coefficient features a hardening at $\sim 200 \, \mathrm{GV}$, as suggested by the light-nucl…
We propose a machine learning method to investigate the propagation of cosmic rays based on the precisely measured spectra of the primary and secondary cosmic ray nuclei of Li, Be, B, C, and O from AMS-02, ACE, and Voyager-1. We train two convolutional neural networks. One network learns how to infer propagation and source parameters from the energy spectra of cosmic rays, and the other network, which is similar to the former, has the flexibility to learn from the data with added artificial fluctuations. Together with the simulated data generated by GALPROP, we find that both networks can prop…
Until fairly recently, it was widely accepted that local cosmic ray spectra were largely featureless power laws, containing limited information on their acceleration and transport. This viewpoint is currently being revised in the light of evidence for a variety of spectral breaks in the fluxes of cosmic ray nuclei. Here, we focus on cosmic ray electrons and positrons which at the highest energies must be of local origin due to strong radiative losses. We consider a pure diffusion model for their Galactic transport and determine its free parameters by fitting data in a wide energy range: measur…
Local interstellar spectra (LIS) of primary cosmic ray (CR) nuclei, such as helium, oxygen, and mostly primary carbon are derived for the rigidity range from 10 MV to ~200 TV using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HelMod, are combined into a single framework that is used to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. The developed iterative maximum-likelihood method uses G…
Revisiting electron-capture decay for Galactic cosmic-ray data
Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）；LPSC, Université Grenoble Alpes, CNRS/IN2P3（格勒诺布尔阿尔卑斯大学法国国家科学研究中心/法国国家粒子与核物理研究所科学宇宙学实验室）
